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The Scientific World Journal
Volume 2014, Article ID 746451, 27 pages
http://dx.doi.org/10.1155/2014/746451
Research Article

Comparative Performance of Four Single Extreme Outlier Discordancy Tests from Monte Carlo Simulations

1Departamento de Sistemas Energéticos, Instituto de Energías Renovables, Universidad Nacional Autónoma de México, 62580 Temixco, MOR, Mexico
2Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, 62209 Cuernavaca, MOR, Mexico
3Posgrado en Ciencias, Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, 62209 Cuernavaca, MOR, Mexico
4Departamento de Computación, Instituto de Energías Renovables, Universidad Nacional Autónoma de México, 62580 Temixco, MOR, Mexico

Received 18 October 2013; Accepted 5 December 2013; Published 11 March 2014

Academic Editors: J. Pacheco and Z. Wu

Copyright © 2014 Surendra P. Verma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Using highly precise and accurate Monte Carlo simulations of 20,000,000 replications and 102 independent simulation experiments with extremely low simulation errors and total uncertainties, we evaluated the performance of four single outlier discordancy tests (Grubbs test N2, Dixon test N8, skewness test N14, and kurtosis test N15) for normal samples of sizes 5 to 20. Statistical contaminations of a single observation resulting from parameters called from ±0.1 up to ±20 for modeling the slippage of central tendency or from ±1.1 up to ±200 for slippage of dispersion, as well as no contamination ( and ), were simulated. Because of the use of precise and accurate random and normally distributed simulated data, very large replications, and a large number of independent experiments, this paper presents a novel approach for precise and accurate estimations of power functions of four popular discordancy tests and, therefore, should not be considered as a simple simulation exercise unrelated to probability and statistics. From both criteria of the Power of Test proposed by Hayes and Kinsella and the Test Performance Criterion of Barnett and Lewis, Dixon test N8 performs less well than the other three tests. The overall performance of these four tests could be summarized as .